The Aviva Premiership champions are puzzled as to why the Montpellier pre-season match was not included in the ban and they remain "disappointed" by the Rugby Football Union's conduct in the case.
Cockerill was banned after being found guilty of unprofessional behaviour and using "extensive foul language" in a touchline exchange with fourth official Stuart Terheege during the Premiership final.
The suspension initially began with the first game of the new Premiership campaign. In contrast, Dylan Hartley's suspension for being sent off in the same game included pre-season matches.
Leicester did not appeal the verdict, only the sanction.
In a club statement, the Tigers said: "We are pleased that the judgement vindicated our decision to appeal and we are grateful to the panel for the consideration that they showed, although we await with interest the written judgement to see why the pre-season game against Montpellier falls into a different category than those against Jersey and Ulster.
"We remain disappointed with the RFU's conduct in this matter but, as we have previously stated, this is a matter we shall pursue privately.
"The focus now is on the remainder of our pre-season and our preparations for the start of the new season."
One of Leicester's frustrations with the RFU is understood to be the length of time it took them to charge Cockerill and then hold the initial disciplinary hearing.
- Sports & Recreation
- Aviva Premiership